All Leaving Cert Mathematics posts
• #### Length-Area-Volume: Triangle Problem. tippytoes

"If the height of a triangle is 5cm less than the length of it's base and if the area of the triangle is 52cm squared, find the length of the base and also the height of the triangle."

I have tried so many different ways and formulas and nothing seems to work for me. I get so far and then have no idea what to do next.

Any help would be greatly appreciated.

1. #### joe9712

by height I'm assuming it means perpendicular,

so 52=(0.5).(x).(x+5)

104=(x^2)+(5X)

factors are (x+13)(x-8)

reject negative answer because length must be positive

so x=8...

2. #### tippytoes

Yes, it means perpendicular.

This is what I got so far:

(b=base h=height/perpendicular. Area of triangle =1/2b x perpendicular hight.)

1/2b x b-5 (h)=52cm squared.

b(b-5) =104 (not sure how I managed to get this)

b^2 -5b =104

b^2-5b-104= 0

But after that I get lost. I can't seem to figure out how to get the 13 and the 8. It is quite annoying :P

3. #### eimearhickey

therefore b= -13 and b= 8

since you cant have negative area your anwer is 8

4. #### joe9712

you just factorise, use the minus b formula or just do it in your head..

5. #### eimearhickey

you can do either but what i normally do is a 5 second rule so if it's not obvious what the factors are I use the minus b formula but since joe 9721 had it already factorised it i just used his figures. For ths question i probably would have used the minus b but any of the three ways would have worked

6. #### tippytoes

Ok, thanks so much. Everything was a great help!

7. #### tippytoes

Would anyone be able to factorise it simply for me, one step at a time. I'm getting confused with some of the steps and mixing things it up.

I'm still a bit lost as to where to get the 13 and the 8. So if someone could write out each step, it would be brilliant, thanks!

8. #### joe9712

It's a pretty general question so I found it online, saves having to write it out!

http://purplemath.com/modules/perimetr3.htm

9. #### tippytoes

Thanks so much! That was a great help!